Choquet integrals, Hausdorff content and fractional operators
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916487405502464 |
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| author | Hatano, Naoya Kawasumi, Ryota Saito, Hiroki Tanaka, Hitoshi |
| author_facet | Hatano, Naoya Kawasumi, Ryota Saito, Hiroki Tanaka, Hitoshi |
| contents | It is shown that the fractional integral operator $I_α$, $0<α<n$, and the fractional maximal operator $M_α$, $0\leα<n$, are bounded on weak Choquet spaces with respect to Hausdorff content. We also investigate these operators on Choquet-Morrey spaces. These results are extensions of the previous works due to Adams, Orobitg and Verdera, and Tang. The results for the fractional integral operator $I_α$ are essentially new. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00915 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Choquet integrals, Hausdorff content and fractional operators Hatano, Naoya Kawasumi, Ryota Saito, Hiroki Tanaka, Hitoshi Functional Analysis 42B25 It is shown that the fractional integral operator $I_α$, $0<α<n$, and the fractional maximal operator $M_α$, $0\leα<n$, are bounded on weak Choquet spaces with respect to Hausdorff content. We also investigate these operators on Choquet-Morrey spaces. These results are extensions of the previous works due to Adams, Orobitg and Verdera, and Tang. The results for the fractional integral operator $I_α$ are essentially new. |
| title | Choquet integrals, Hausdorff content and fractional operators |
| topic | Functional Analysis 42B25 |
| url | https://arxiv.org/abs/2308.00915 |